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Simplifying 3 + 7(x + -3) = 6(x + -3)(x + -3) Reorder the terms: 3 + 7(-3 + x) = 6(x + -3)(x + -3) 3 + (-3 * 7 + x * 7) = 6(x + -3)(x + -3) 3 + (-21 + 7x) = 6(x + -3)(x + -3) Combine like terms: 3 + -21 = -18 -18 + 7x = 6(x + -3)(x + -3) Reorder the terms: -18 + 7x = 6(-3 + x)(x + -3) Reorder the terms: -18 + 7x = 6(-3 + x)(-3 + x) Multiply (-3 + x) * (-3 + x) -18 + 7x = 6(-3(-3 + x) + x(-3 + x)) -18 + 7x = 6((-3 * -3 + x * -3) + x(-3 + x)) -18 + 7x = 6((9 + -3x) + x(-3 + x)) -18 + 7x = 6(9 + -3x + (-3 * x + x * x)) -18 + 7x = 6(9 + -3x + (-3x + x2)) Combine like terms: -3x + -3x = -6x -18 + 7x = 6(9 + -6x + x2) -18 + 7x = (9 * 6 + -6x * 6 + x2 * 6) -18 + 7x = (54 + -36x + 6x2) Solving -18 + 7x = 54 + -36x + 6x2 Solving for variable 'x'. Reorder the terms: -18 + -54 + 7x + 36x + -6x2 = 54 + -36x + 6x2 + -54 + 36x + -6x2 Combine like terms: -18 + -54 = -72 -72 + 7x + 36x + -6x2 = 54 + -36x + 6x2 + -54 + 36x + -6x2 Combine like terms: 7x + 36x = 43x -72 + 43x + -6x2 = 54 + -36x + 6x2 + -54 + 36x + -6x2 Reorder the terms: -72 + 43x + -6x2 = 54 + -54 + -36x + 36x + 6x2 + -6x2 Combine like terms: 54 + -54 = 0 -72 + 43x + -6x2 = 0 + -36x + 36x + 6x2 + -6x2 -72 + 43x + -6x2 = -36x + 36x + 6x2 + -6x2 Combine like terms: -36x + 36x = 0 -72 + 43x + -6x2 = 0 + 6x2 + -6x2 -72 + 43x + -6x2 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 -72 + 43x + -6x2 = 0 Factor a trinomial. (-9 + 2x)(8 + -3x) = 0Subproblem 1
Set the factor '(-9 + 2x)' equal to zero and attempt to solve: Simplifying -9 + 2x = 0 Solving -9 + 2x = 0 Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + 2x = 0 + 9 Combine like terms: -9 + 9 = 0 0 + 2x = 0 + 9 2x = 0 + 9 Combine like terms: 0 + 9 = 9 2x = 9 Divide each side by '2'. x = 4.5 Simplifying x = 4.5Subproblem 2
Set the factor '(8 + -3x)' equal to zero and attempt to solve: Simplifying 8 + -3x = 0 Solving 8 + -3x = 0 Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -3x = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -3x = 0 + -8 -3x = 0 + -8 Combine like terms: 0 + -8 = -8 -3x = -8 Divide each side by '-3'. x = 2.666666667 Simplifying x = 2.666666667Solution
x = {4.5, 2.666666667}
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